Abstract
We provide the representation of quasi-periodic solutions of periodic Dirac equations in terms of the spectral parameter power series (SPPS) recently introduced by V.V. Kravchenko [1, 2, 3]. We also give the SPPS form of the Dirac Hill discriminant under the Darboux nodeless transformation using the SPPS form of the discriminant. and apply the results to one of Razavy’s quasi-exactly solvable periodic potentials.
Mathematics Subject Classification (2000).Primary 34B24; Secondary 34C25.
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Khmelnytskaya, K.V., Rosu, H.C. (2012). Bloch Solutions of Periodic Dirac Equations in SPPS Form. In: Ball, J., Curto, R., Grudsky, S., Helton, J., Quiroga-Barranco, R., Vasilevski, N. (eds) Recent Progress in Operator Theory and Its Applications. Operator Theory: Advances and Applications(), vol 220. Springer, Basel. https://doi.org/10.1007/978-3-0348-0346-5_9
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DOI: https://doi.org/10.1007/978-3-0348-0346-5_9
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